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I use the thing on the left of this next picture. You make an X using the center find attachment and where the lines cross is the center. Do this line with a sharp scribe and your center punch can be felt to fall into the groove made by the scribe.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Thank you to our families of soldiers, many of whom have given so much more then the rest of us for the Freedom we enjoy.

It is true, there is nothing free about freedom, don't be so quick to give it away.

None of those instruments will find the centre unless they are accurate. If in doubt scribe three lines with the tool at about 120 degree angles. If they all cross at the same point the device is accurate, if you get a small triangle scribed the centre is in the middle of the triangle.

Even though the instrument may be accurate the end result depends on skill with the scriber.

how exact?

I'll probably take some grief for this,but how exact a center (or centre) are you hunting? I've learned (alot of it from this forum) that an exact center for a fabricator and a center for a watchmaker are to VERY different points.The instruments shown in the other posts are more than accurate enough for the fab stuff I do,even taking into consideration failing eyesight. However,they may not produce the results needed for someone re-manning a a turbo,so I guess its a question of of thousandths or tens?

The simplest tool is a center punch that comes out of a funnel.
You stick the concave funnel shape onto the end of a round shaft and hit the punch, and its done. I don't have a photo to show you

When not using the Lathe for such an assignment, and location is not super critical, I lay the round down on the workbench and place a tool bit about half the diameter on the bench at the end of the shaft.
roll the round back and forth, and using a felt tip maker on top of the tool bit, I draw a series of horizontal lines OR if the felt tip is large, just hold it near the center of the round.
The felt tip will actually be slightly above C/L
When you remove the round , you have a nice shiney spot exactly in the middle of the round. This can be a very accurate measure, when you use a spring punch on the shinney part before center punching